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Law of large numbers and large deviations for dependent risks

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  • Ramona Maier
  • Mario Wuthrich

Abstract

We analyse the mathematical structure of models for large risk portfolios, especially for credit risk models. These risk portfolios are modelled using a multivariate mixture model for the dependence structure between the risks. The dependence structures are characterized by latent variables Θ, which play the role of systematic risks. We show that, depending on the choice of the distribution of Θ, there are different asymptotic behaviours for the aggregated risk portfolio, namely law of large numbers/central limit theorem behaviour and large deviation behaviour.

Suggested Citation

  • Ramona Maier & Mario Wuthrich, 2009. "Law of large numbers and large deviations for dependent risks," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 207-215.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:2:p:207-215
    DOI: 10.1080/14697680801986587
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    References listed on IDEAS

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    1. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
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    Cited by:

    1. Georg Ch. Pflug & Alois Pichler, 2018. "Systemic risk and copula models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(2), pages 465-483, June.

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